5.8 polynomial equations - solving equations by factoring
DESCRIPTION
5.8 Polynomial Equations - Solving Equations by Factoring. Solutions to Equations in One Variable: Where the curve crosses the x-Axis (if it does!) Solving Quadratic Equations ax 2 + bx + c = 0 Zero factor property Solving Higher Degree Equations Problem Solving - PowerPoint PPT PresentationTRANSCRIPT
5.8 1
5.8 Polynomial Equations - Solving Equations by Factoring Solutions to Equations in One Variable:
Where the curve crosses the x-Axis (if it does!) Solving Quadratic Equations
ax2 + bx + c = 0 Zero factor property
Solving Higher Degree Equations Problem Solving Not covered:
Functions/Graphs
5.8 2
Curves and x-Intercepts y=x+3 y=x2 y=x3 y=|x|
5.8 3
Definition
Zero Factor Property
5.8 4
Solving a Quadratic Equation by Factoring
5.8 5
solutionsrationalNorationalsoverfactorCannot
x
x
03
32
2
75
34 &
057&0430)57)(43(
xxxx
xx
solutionOnlyxandx
xxx
144
0)4(0168
2
2
23
43
2
&0)32)(34(
6126720968
9)34(2
yyyy
yysobacyy
yy
Examples: 0, 1, or 2 solutions
RewriteFactorSet Each = 0Solve EachCheck
Unfactorable quadratics are prime and have no rational number solutions.
5.8 6
solutionsrationalNoRationalsoverfactorableNot
x
x
07
72
2
2&0)2)(16(
02116
2)42(3
61
2
xxxx
factoringerrorandtrialxx
xxx
43&3034&03
0)34)(3(
xxxx
xx
solutionOnlyzz
zzz
11&1
0)1(012
2
2
Practice: 0, 1, or 2 solutions
RewriteFactorSet Each = 0Solve EachCheck
Unfactorable quadratics are prime and have no rational number solutions.
5.8 7
Higher Degree Polynomial Equations Write in descending powers of the variable = 0 Make leading coefficient positive (multiply by -1) Factor Solve each factor = 0 May have 0 to n (the degree) solutions Check all solutions in original equation
5.8 83,20)3)(3)(2)(2(
0)9)(4(0361301336
22
24
24
aaaaaa
aaaa
aa
1sec
0)1)(1(
012
3
xsolutionOneprimeisfactorondthe
xxx
x
Examples, 0 to n solutions
RewriteFactorSet Each = 0Solve EachCheck
Unfactorable quadratics are prime and have no rational number solutions.
3,,00)3)(25(0)6135(
6135
52
2
23
xxxxxxxxx
xxx
5.8 9
2sec
0)42)(2(
082
3
bsolutionOneprimeisfactorondthe
bbb
b
Practice, 0 to n solutions
RewriteFactorSet Each = 0Solve EachCheck
Unfactorable quadratics are prime and have no rational number solutions.
2,2,00)2)(2(2
0)4(26682
2
3
xxxxxx
xxxx
5,20)5)(5)(2)(2(
0)25)(4(010029029100
22
24
24
xxxxxx
xxxx
xx
5.8 10
Integers Consecutive Integers:
n, n+1, n+2, n+3, … Consecutive
Even or Odd Integers:n, n+2, n+4, n+6, …
Find 3 consecutive odd integers where the product of the first 2 is 68 more than the 3rd integer.
5,7,9,6363685)7(9
'8980)9)(8(
072
722
684)2(
2
2
so
oddtisnnandn
nnnn
nnn
nnn
5.8 11'5611'12618
3)(5.11)3)(232(20)69292(20
1385840
4223619860
)211)(218(60)(
2
2
2
LWborfalseb
bbbb
bb
bbb
bbwidthborderbWLA
Borders
5.8 12
Gravity
SLINGSHOT A slingshot can provide an initial velocity of 128 feet per second. At what times will a stone, shot vertically upward, be 192 feet above the ground? sandtimesAt
tttt
tt
tt
tvth
sec'620)6)(2(160)128(16
019212816
16128192
16
2
2
2
2
5.8 13
What Next? 6.1 Rational Expressions
Look for patterns …